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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. "
Plane Geometry - Page 180
by Arthur Schultze - 1901
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...triangles are similar, Given ^A'. 282 282 A A'B'C' A'B' X A'C' (The areas of two triangles that have an angle of the one equal to an angle of the...products of the sides including the equal angles.) 4 AABC AB AC 1S> A A'R'r' — T7^ x ~Arr]' ii Ji. Jj \j . I /* AL AB AC (Similar polygons have their...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...Given .'.ZA = ZA'. 282 Then AABC AB * AC 111611 AA'B'C' ~ AW X A'C" (The areas of two triangles that have an angle of the one equal to an angle of the...products of the sides including the equal angles.) AABC AB AC But f = I^' 282 (Similar polygons have their corresponding sides proportional.) Substituting...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...cross section ? 193. Theorem IV. Two triangles that have an acute angle of the one equal to an acute angle of the other are to each other as the products of the sides including the equal angles. C B' BD FIG. 134 Given the A ABC and A'B'C having the ZC common. Proof. DrawAB'. Then, since the triangles...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...vertices of an inscribed rectangle inclose a rhombus. Ex. 1067. Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional. Ex. 1068. Two rectangles are similar if two adjacent sides are...
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Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...Theorem XVIII. Two triangular pyramids that have a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the edges including the equal trihedral angles. Given the triangular pyramids O-FGH and O'-FG'H', with...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...one are equal respectively to two angles of the other. PROPOSITION XIV. THEOREM 288. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. BA ~ & Given the triangles ABC and A'B'C',...
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Connecticut School Document, Issues 1-13

Education - 1913 - 396 pages
...only one If two triangles have their homologous sides proportional they are similar If two triangles have an angle of the one equal to an angle of the other their areas are to each other as the products of the sides including the equal angles The area of a...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...632. The volumes of two triangular pyramids, that have a trihedral angle of one equal to a trihedral angle of the other, are to each other as the products of the three edges of these angles. Given V and v', volumes of the triangular pyramids 0-ABC and O'-EFG, having...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...327. Corollary 1. Two triangular prisms that have a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the edges including the trihedral angles. [HINT. Break the prism up into triangular pyramids, and use ...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...vertices of an inscribed rectangle inclose a rhombus. Ex. 1067. Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional. Ex. 1068. Two rectangles are similar if two adjacent sides are...
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